Methyl hydrate is a synonym for methanol (or methyl alcohol, or wood
alcohol, or carbinol).  It does not mix well with mineral oil.
Paint thinner is usually mineral spirits or petroleum spirits, a mixture of
various naphtha compounds.  I don't have any handy, and have not tried it,
but I expect it would mix well with mineral oil, since most other
hydrocarbon-type solvents do.
Paul M.